
(/VERSIONCHECK 2) 

(DEFPARAMETER |OctonionCategory;CAT| 'NIL) 

(DEFPARAMETER |OctonionCategory;AL| 'NIL) 

(DEFUN |OctonionCategory| (#1=#:G1863)
  (LET (#2=#:G1864)
    (COND
     ((SETQ #2# (|assoc| #3=(|devaluate| #1#) |OctonionCategory;AL|))
      (CDR #2#))
     (T
      (SETQ |OctonionCategory;AL|
              (|cons5| (CONS #3# (SETQ #2# (|OctonionCategory;| #1#)))
                       |OctonionCategory;AL|))
      #2#)))) 

(DEFUN |OctonionCategory;| (|t#1|)
  (PROG (#1=#:G1862)
    (RETURN
     (PROG1
         (LETT #1#
               (|sublisV| (PAIR '(|t#1|) (LIST (|devaluate| |t#1|)))
                          (COND (|OctonionCategory;CAT|)
                                ('T
                                 (LETT |OctonionCategory;CAT|
                                       (|Join| (|Algebra| '|t#1|)
                                               (|FullyRetractableTo| '|t#1|)
                                               (|FullyEvalableOver| '|t#1|)
                                               (|mkCategory|
                                                '(((|conjugate| ($ $)) T)
                                                  ((|real| (|t#1| $)) T)
                                                  ((|imagi| (|t#1| $)) T)
                                                  ((|imagj| (|t#1| $)) T)
                                                  ((|imagk| (|t#1| $)) T)
                                                  ((|imagE| (|t#1| $)) T)
                                                  ((|imagI| (|t#1| $)) T)
                                                  ((|imagJ| (|t#1| $)) T)
                                                  ((|imagK| (|t#1| $)) T)
                                                  ((|norm| (|t#1| $)) T)
                                                  ((|octon|
                                                    ($ |t#1| |t#1| |t#1| |t#1|
                                                     |t#1| |t#1| |t#1| |t#1|))
                                                   T)
                                                  ((|abs| (|t#1| $))
                                                   (|has| |t#1|
                                                          (|RealNumberSystem|)))
                                                  ((|rational?|
                                                    ((|Boolean|) $))
                                                   (|has| |t#1|
                                                          (|IntegerNumberSystem|)))
                                                  ((|rational|
                                                    ((|Fraction| (|Integer|))
                                                     $))
                                                   (|has| |t#1|
                                                          (|IntegerNumberSystem|)))
                                                  ((|rationalIfCan|
                                                    ((|Union|
                                                      (|Fraction| (|Integer|))
                                                      "failed")
                                                     $))
                                                   (|has| |t#1|
                                                          (|IntegerNumberSystem|)))
                                                  ((|inv| ($ $))
                                                   (|has| |t#1| (|Field|))))
                                                '(((|Finite|)
                                                   (|has| |t#1| (|Finite|)))
                                                  ((|OrderedSet|)
                                                   (|has| |t#1|
                                                          (|OrderedSet|)))
                                                  ((|ConvertibleTo|
                                                    (|InputForm|))
                                                   (|has| |t#1|
                                                          (|ConvertibleTo|
                                                           (|InputForm|))))
                                                  ((|CharacteristicZero|)
                                                   (|has| |t#1|
                                                          (|CharacteristicZero|)))
                                                  ((|CharacteristicNonZero|)
                                                   (|has| |t#1|
                                                          (|CharacteristicNonZero|))))
                                                '((|Fraction| (|Integer|))
                                                  (|Boolean|))
                                                NIL))
                                       . #2=(|OctonionCategory|)))))
               . #2#)
       (SETELT #1# 0 (LIST '|OctonionCategory| (|devaluate| |t#1|))))))) 
